Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
| direct product | Dic10×C22⋊A4 |
| unambiguous semidirect product | C5⋊(Q8×C22⋊A4) |
| Hall | C24×Dic10 ⋊ C3 |
| Sylow | C5 ⋊ Q8×C22⋊A4 |
2228 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 2228 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
104 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240372);